How do you try different random seeds for noise texture node?
This doesn't really change the seed, but you can get a different noise pattern by translating the whole texture by a significant amount.



The Suzanne on the left uses a noise texture with default settings and mapping coordinates.  The Suzanne on the right uses the same noise texture, but uses the below nodes to shift the texture coordinates to get a different noise pattern.



For the sake of space i am using my homemade translate node but you could just as well use a mapping node as well.